Convergence Rates for Uniform B-Spline Density Estimators Part I: One Dimension

Autor:	Richard A. Redner
Rok vydání:	1999
Předmět:	Computational Mathematics Spline (mathematics) Mathematical optimization Metric space Rate of convergence Applied Mathematics B-spline Nonparametric statistics Applied mathematics Estimator Probability density function Moment-generating function Mathematics
Zdroj:	SIAM Journal on Scientific Computing. 20:1929-1953
ISSN:	1095-7197 1064-8275
DOI:	10.1137/s1064827595291996
Popis:	A B-spline nonparametric density estimator with uniform knots, convenient for solving problems in computer graphics, was discussed by Gehringer and Redner in 1992 [ Comm. Stat. Simulation Methods, 21 (1992) pp. 849--878]. These ideas were later extended to density function estimation on metric spaces using partitions of unity in Redner and Gehringer in 1994 [Comm. Stat. Theory Methods, 23 (1994) pp. 2059--2076]. In the current paper we return to the uniform B-spline density estimator in one dimension. We show, under very natural assumptions, that the B-spline density estimator and all of its nontrivial derivatives converge in mean integrated squared error. Asymptotic rates of convergence are determined for the density estimate and its derivatives.
Databáze:	OpenAIRE
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